diff --git a/R/knnDE.R b/R/knnDE.R
index 5f57519..d2e5c65 100644
--- a/R/knnDE.R
+++ b/R/knnDE.R
@@ -1,6 +1,19 @@
+#' @title knnDE
+#'
+#' @param X an n by d matrix of coordinates containing points used int the
+#' density estimation, where n is the number of points and d is the dimension
+#'
+#' @param Grid an m by d matrix of coordinates, where m is the number of points
+#' in the grid and d is the dimension
+#'
+#' @param k a number used as the smoothing parameter
+#'
+#' @return a vector of length m (number of points in Grid) containing the value
+#' of the knn Density Estimator for each point in the grid
+
 knnDE <-
 function(X, Grid, k){
-
+  
   if (!is.numeric(X) && !is.data.frame(X)) {
     stop("X should be a matrix of coordinates")
   }
@@ -11,10 +24,16 @@ function(X, Grid, k){
     stop("k should be a positive integer")
   }
 
+  # store d, the dimension of X, and n, the number of points in X
   d <- ncol(X)
   n <- nrow(X)
+  # find the Euclidean distances of k nearest neighbors from input matrix X and the query matrix
+  # Grid using the fast nearest neighbor searching algorithm "kd_tree"
   r.k <- apply(FNN::knnx.dist(X, Grid, k = k, algorithm = "kd_tree"), 1, max)
+  # volume of the Euclidean d dimensional unit ball
   v.d <- pi^(d/2) /gamma(d/2+1)
+  # final output incorporates smoothing parameter with volume of unit ball and euclidean k nearest neighbor
+  # distances to return output vector containing density estimators for each point in the grid
   out <- k / (n * v.d * r.k ^ d)  
   return(out)
-}
\ No newline at end of file
+}